Abstract
The problem of describing adjacency on the set of orbits of a Borel subgroup B of a reductive group G acting on a spherical variety (that is, a G-variety with a finite number of B-orbits) is considered. The adjacency relation on the set of B-orbits generalizes the classical Bruhat order on the Weyl group. For a special class of homogeneous spherical varieties G/H, where H is a product of a maximal torus and the commutator subgroup of a maximal unipotent subgroup of the group G, a satisfactory description of the set of B-orbits with adjacency relation is obtained.
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